Here's one better. It's a type 2 diabetes study that compared exercise against metformin against a placebo. The conclusions were so overwhelmingly in favor of exercise that the study was stopped early.
Two of four subtasks that reflect complex cognitive speed (Stroop color/word interference and Concept Shifting Test) showed main and interaction effects with age of aerobic capacity in a hierarchical regression analysis, accounting for up to 5% of variance in parameter score after correction for age, sex, and intelligence main effects.
Still, that study is rather weak evidence. The benefits could be relegated to preventing decline in older people. Anecdotally, I do feel duller on days when I don't run; even if I didn't, I'd still exercise. It helps me relieve stress.
In terms of general benefits, most people would be better off if they exercised more, not less. I mean it's not like fit people wake up one day, look at a mirror and see a firm, toned body with six-pack abs then scream at the sky, "Nooooo! Why me?!"
...really? It seems stunningly obvious to me that exercise and a good diet is good for overall health and mental health. I think the burden of proof is on you here. Or are you just positing that exercise+diet has no impact on productivity, not health?
Here's one better. It's a type 2 diabetes study that compared exercise against metformin against a placebo. The conclusions were so overwhelmingly in favor of exercise that the study was stopped early.